The Blues had already had an initial bid of £20m ($31.1m) rejected by the Toffees, according to the Mirror, and they are said to be holding out for a record fee of around £34m ($53m) despite the club insisting that the player is not for sale.

Jose Mourinho has publicly expressed interest in signing the young English defender, whom he views as the ideal long-term replacement for John Terry, who despite signing a new contract, turns 35 this year.

"We made a bid, the bid is there and Everton have the power to accept it or refuse it," Mourinho told Sky Sports.

"This is between John Stones and Everton and I don't speak about him because he is an Everton player."

"If we made a bid it is because we like the player, we don't make bids for players we don't like, but we respect Everton and respect every club that has a player and it is up to them - everything is in their hands," the Portuguese manager added.

Stones has established himself as a regular starter after impressing last season, and with four-years still remaining on his current deal the Merseyside club will be reluctant to let one of their brightest stars leave the club.

The report claims that Manchester United have also entered the race to sign the England international, and have supposedly contacted the intermediaries working on Stones' behalf to inform them about the Red Devils' interest in taking him to Old Trafford.

Louis van Gaal is also on the market for a central defender, but is yet to submit a formal offer for Stones, with the report claiming that Chelsea are still leading the race for the defender's signature.

According to the Mirror, the Premier League champions will prepare a third bid as Mourinho is keen to complete the deal before the start of the new campaign, with an ESPN report suggesting that Chelsea are confident of taking the defender to Stamford Bridge this summer.